都計系/工設系微積分課程介紹
課程名稱：大一微積分(一學期)
課程時間：星期一 9:10-11:00；星期三 8:10-9:00 上課地點：都計館(50102)
研討時間: 星期三 9:10-10:00 研討地點：唯農館 7213, 7215, 7217 授課教師：許瑞麟老師
辦公室： 許瑞麟 : 數學系館 408
Email： 許瑞麟 : rsheu@mail.ncku.edu.tw 電話：許瑞麟 : 2757575-65150 助教: 林威溢, 林剛玄, 馮若梅
林威溢助教辦公室：數學系館 411
Email： hajime.tw@gmail.com 電話：2757575-65156-411 林剛玄助教辦公室：數學系館 418
Email： spybeiman@gmail.com 電話：2757575-65156-418 馮若梅助教辦公室：數學系館 411
Email： coolmint60431@hotmail.com 電話：2757575-65156-411
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預備知識：高中數學。
指定教科書：“Applied Calculus for the life and social sciences” by Ron Larson。
教科書購買請找廖怡華小姐~ 手機 : 0980-081069; 0953-575655 其他工具: 工程用計算機, 上課考試用到。
課程內容綱要：這是一個學期介紹微積分的課程。我們不會特別強調定理的證 明，而是注重實際例子的應用，以及計算。主要內容請詳見指定 教材的目錄。在一個學期內我們預定講授指定教材第一到第七 章，以及第九,十兩章。
上 課 方 式 : 兩 系 併 成 大 班 上 課，但分 三 小 班 研 討。上課由教授講解課程觀 念內容，演習課由助教講解習題，或請同學上台做，或舉行小考。
成績計算方式：二次期中考各佔 22.5%，一次期末考佔 35%，平時成績佔 20%。
黃卡(Yellow Card)加分: 每人有屬於自己的一張黃卡，用來鼓勵同學發問問題。
課間, 課後, 演習課, 老師/助教 office hour 等問問題，每次可獲 得教授/助教一個簽名。每個簽名可獲得總成績加分 0.75 分。加 分以 20 分為上限。黃卡於期末考前繳回。
出席與點名: 每堂課(含教授上課以及助教演習課)不定期點名。發考卷等同點名, 不得代拿. 點名一次不到以曠課 1 小時論, 扣期末總成績一分. 曠
課超過 1/9, 期末扣考. 缺席曠課罰則依成功大學學則之相關規定 辦理. 請參閱網址:
http://www.ncku.edu.tw/%7Eregister/chinese/a1.htm.
Office Hours: 每星期一 11:20 – 11:50. 這是你和老師面對面溝通的機會. 歡迎任 何問題, 數學或非數學. 請事先以 e-mail, 電話, 或當面敲定時間, 以免撲空或久候. 助教之 Office Hours 另訂之.
考試時間與範圍：
第一次期中考 10 月 14 日 0.1 – 3.3 第二次期中考 11 月 30 日 3.4 – 7.1
期末考 1 月 11 日 第二次期中考前範圍佔 30%, 之後 70%.
預定的進度如下：
第一週 (9/14-9/16) (9/14) 課程規定宣導. 0.1Real number systems, 1.1 – 1.2 The Cartesian Plane and graphs of equations; 1-4 functions (9/16) 1-5 limits.
第二週 (9/21-9/23) (9/20) 1-6 continuity; 2-1 The derivative;
(9/23) 2-2 Some rules of differentiations
第三週 (9/28-9/30) (9/28) 2-3 Rate of Changes; 2-4 The product and Quotient Rule;
(9/30) 2-5 The chain rules; 2-6 higher order derivatives 第四週 (10/5-10/7) (10/5) 3-1 increasing and decreasing functions, critical
points 3-2 Extrema and the first derivative test;
(10/7) 3-3 Concavity 第五週 (10/12-10/14) (10/12) 停課.
(10/14) 期中考
第六週 (10/19-10/21) (10/19) 3-4 Asymptotes
(10/21) 4-2 Natural exponential functions;
第七週 (10/26-10/28) (10/26) 4-3 Derivative of exponential functions 4-5 Derivative of log functions.
(10/28) 4-6 Exponential growth and decay 第八週 (11/2-11/4) (11/2) 5-3 Graphs of trigonometric functions; 5-4
Derivatives of trigonometric functions
(11/4) 6-1 Antiderivatives and indefinite integral 第九週 (11/9-11/11) (11/9) 6-3 Exponential and Logarithmic integrals.
(11/11) 校慶停課
第十週 (11/16-11/18) (11/16) 6-4 Fundemental Theorem of Calculus.
(11/18) 6-4 Fundemental Theorem of Calculus.
第十一週 (11/23-11/25) (11/23) 6-6 Volumes of Solids of revolution.
(11/25) 7-1 Integration by parts;.
第十二週 (11/30-12/2) (11/30) 期中考.
(12/2) 7-2 logistic growth;
第十三週 (12/7-12/9) (12/7) 7-3 Integral of trigonometric functions . (12/9) 9-1 The three dimensional coordinate system 第十四週 (12/14-12/16) (12/14).9-2 Surfaces in Space
(12/16) 9-3 Functions of several variables 第十五週 (12/21-12/23) (12/21) 9-4 Partial derivatives.
(12/23) 9-5 Extrema of functions of two variables 第十六週 (12/28-12/30) (12/28) 10-1 solutions of differential equations,
(12/30) 10-2 separation of variables
第十七週 (1/4-1/6) (1/4) 10-4 application of differential equations (1/6) 10-4 application of differential equations 第十八週 (1/11) (1/11)期末考
指定習題：
§0.1: 5, 7, 13, 19, 21, 25, 27, 31, 37
§1.1: 1, 7, 13, 15, 19, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43
§1.2: 1, 5, 7, 11, 13, 19, 21, 25, 29, 35, 39, 43, 47, 51, 55, 61, 63, 65, 69, 70, 73, 74
§1.4: 1, 5, 9, 13, 15, 19, 23, 27, 29, 33, 39, 41, 45, 49, 55, 63, 65, 66, 69, 70, 73, 75
§1.5: 1, 5, 9, 11, 13, 15, 17, 23, 33, 35, 37, 43, 51, 53, 63, 65, 73
§1.6: 1, 3, 5, 7, 11, 15, 19, 23, 27, 29, 31, 35, 41, 43, 49, 51, 55, 56, 59, 61, 63
§2.1: 3, 5, 11, 14, 17, 23, 26, 29, 33, 35, 37, 41, 43, 45, 51, 55, 66, 67, 68, 69, 71, 73
§2.2: 1, 3, 7, 9, 11, 17, 21, 27, 31, 33, 37, 41, 45, 47, 51, 53, 55, 57, 58, 61, 65, 67
§2.3: 1, 3, 7, 11,15, 17, 19, 23, 27
§2.4: 1, 5, 9, 11, 15, 21, 23, 27, 33, 37, 39, 45, 51, 55, 57, 59, 63, 64, 65, 67
§2.5: 1, 7, 9, 11, 13, 17, 23, 33, 39, 43, 51, 57, 59, 63, 67, 69, 71, 79, 81
§2.6: 1, 7, 13, 15, 19, 21, 25, 27, 31, 33, 37, 39, 41, 43, 45, 49, 51, 53, 55, 57
§3.1: 1, 3, 7, 9, 15, 27, 29, 33, 36, 37, 39
§3.2: 1, 3, 5, 9, 13, 19, 23, 27, 33, 37, 39, 41, 43, 46, 47, 47
§3.3: 1, 3, 6, 9, 13, 23, 27, 31, 37, 45, 47, 49, 53, 55, 57, 61, 64, 65
§3.4: 1, 5, 7, 11, 14, 15, 17, 19, 21, 23, 27, 31, 35
§4.2: 1, 3, 5, 11, 13, 16, 17, 19, 27, 31
§4.3: 1, 3, 7, 11, 15, 19, 21, 25, 27, 31, 33, 37, 39, 41, 43, 44, 47
§4.5: 1, 3, 7, 11, 19, 23, 27, 31, 37, 47, 51, 55, 59, 61, 63, 67, 71, 77
§4.6: 1, 3, 7, 11, 15, 17, 19, 21, 23, 25, 31, 33, 37, 39, 41
§5.3: 1, 3, 17, 21, 29, 33, 39, 47, 57, 61, 65, 69, 71, 75, 79, 83, 85
§5.4: 3, 5, 9, 13, 31, 35, 41, 43, 45, 47, 49, 51, 53, 57, 59, 63, 65, 67, 69, 71, 75, 77
§6.1: 1, 3, 7, 11, 18, 19, 21, 23, 27, 31, 35, 39, 43, 47, 51, 53, 55, 57, 61, 63, 73
§6.3: 3, 9, 15, 25, 29, 35, 41, 47, 55, 59, 63
§6.4: 1, 9, 11, 13, 17, 21, 23, 31, 37, 39, 49, 53, 55, 61, 67, 71, 75, 77, 83, 87
§6.6: 1, 5, 11, 15, 19, 25, 27
§7.1: 1, 3, 7, 9, 13, 29, 33, 37, 41, 47, 49, 53, 57, 59, 65
§7.2: 1, 5, 11, 15, 21, 29, 33, 41, 45, 49, 51, 61
§7.3: 1, 7, 25, 27, 35, 39, 45, 51, 53, 63
§9.1: 3, 5, 9, 11, 15, 17, 23, 25, 27, 29, 33, 37, 39, 43, 49, 53, 55, 59
§9.2: 7, 9, 11, 19, 23, 25, 29, 33, 35, 39, 43, 45, 51, 53
§9.3: 3, 7, 11, 13, 15, 17, 27, 29, 31, 35, 39, 49
§9.4: 5, 9, 13, 15, 19, 25, 27, 29, 35, 41, 43, 51, 55, 59, 61, 67
§9.5: 3, 5, 15, 17, 19, 21, 25, 29, 31, 33, 39, 41, 43, 51
§10.1: 7, 11, 13, 23, 25, 26, 27, 28, 33, 35, 38, 39, 47, 55, 56
§10.2: 3, 11, 17, 19, 29, 35, 37, 41, 43, 45, 47, 49, 51
§10.4: 3, 7, 11, 15, 29, 39
